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Cutoff on Trees is Rare

Author

Listed:
  • Nina Gantert

    (Technical University of Munich)

  • Evita Nestoridi

    (Stony Brook University)

  • Dominik Schmid

    (University of Bonn)

Abstract

We study the simple random walk on trees and give estimates on the mixing and relaxation times. Relying on a seminal result by Basu, Hermon and Peres characterizing cutoff on trees, we give geometric criteria that are easy to verify and allow to determine whether the cutoff phenomenon occurs. We provide a general characterization of families of trees with cutoff, and show how our criteria can be used to prove the absence of cutoff for several classes of trees, including spherically symmetric trees, Galton–Watson trees of a fixed height, and sequences of random trees converging to the Brownian continuum random tree.

Suggested Citation

  • Nina Gantert & Evita Nestoridi & Dominik Schmid, 2024. "Cutoff on Trees is Rare," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1417-1444, June.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-023-01274-5
    DOI: 10.1007/s10959-023-01274-5
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